Decomposability, instabilities, and saturation in multiprogramming systems

Abstract

A step-by-step approach to model the dynamic behavior and evaluate the performance of computing systems is proposed. It is based on a technique of variable aggregation and the concept of nearly decomposable systems, both borrowed from Econometrics. This approach is taken in order to identify in multiprogramming paging systems (i) unstable regimes of operations and (ii) critical computing loads which bring the system into states of saturation. This analysis leads to a more complete definition of the circumstances in which "thrashing" can set in. Volume 18Number 7 is the Hrst large one using the RC 4000 multiprogramming system.

Blending randomness in closed queueing network models

“…However, in intermediate cases, we have established by (A.1)-(A.2) that the probability distributions π 1 and π 2 depend also on matrices Q * 1 Q * 2 and Q * 2 Q * 1 , which are not infinitesimal generators, having negative off-diagonal entries. This suggests that there may not exist a simple way to approximate well in all cases π 1 and π 2 based on weighting of the equilibrium solutions for Q AVG , Q * 1 , or Q * 2 , a strategy that is common in previous work [14,43]. • R h : routing matrix for all stages h = 1, .…”

“…Conversely, in the decomposition approximation, an isolated model is evaluated for each stage of the random environment. The isolated solutions are then weighted across stages using the equilibrium distribution of the random environment [14,43]. This approach describes well an environment where transitions happen rarely compared to the representative timescales of the system (e.g., component failures).…”

Bound analysis of closed queueing networks with workload burstiness

“…In Section 2.2, we evaluate the applicability of approximation algorithms for models with GI service to models with nonrenewal service. Due to limited space, we point the reader to [7,13,22] for general background on queueing network modeling and Markov processes. Throughout this paper we assume that service time distributions are modeled by the method of phases [7,14].…”

“…In [32], Zahorjan et al obtain an approximate mean value analysis (AMVA) by decomposition-aggregation [13]. The underlying Markov process of the network is decomposed according to the active phases at the GI servers.…”

Software Engineering Principles

“…If a process that has been allocated some of resource B is slowed by the monitor that allocates resource A, then the policy used in allocating A may have noticeable effects on the allocation of B. P. J. Courtois (1975; has carefully investigated this problem and developed statistical criteria to help recognize situations where there would be excessive error caused by ignoring the allocation policy for one resource when designing an allocator for another. Very roughly, if we wish to neglect the dynamics of resource A when concerned with resource B, the actions that change the state of resource A must be of short duration and occur relatively frequently when compared to actions that change the state of resource B.…”